Simplifying Fractional Exponents
To simplify the given expression \( \frac{2x^7y}{8x^9y^2} \), you'll need to divide the numerator by the denominator for each variable and the coefficients.
Step 1 - Simplify the coefficients:
Divide the coefficients \(2\) and \(8\):
\[ \frac{2}{8} = \frac{1}{4} \]
Step 2 - Simplify the x terms:
When you divide terms with the same base, you subtract the exponents (according to the law of exponents):
\[ x^7 / x^9 = x^{7-9} = x^{-2} \]
Since a negative exponent indicates that you should take the reciprocal of the base raised to the positive exponent, \( x^{-2} \) can be rewritten as \( 1/x^2 \) if the expression is required to have only positive exponents.
Step 3 - Simplify the y terms:
For the y terms:
\[ y / y^2 = y^{1-2} = y^{-1} \]
Again, for positive exponents, \( y^{-1} \) would be \( 1/y \).
Combining these results, the simplified expression is:
\[ \frac{1}{4} \cdot \frac{1}{x^2} \cdot \frac{1}{y} \]
Or more simply:
\[ \frac{1}{4x^2y} \]
This is your final simplified expression.
